Question

Prove that the following functions do not have maxima or minima:
h(x) = x³ + x² + x +1

Answer 1

Step-by-step explanation:

ANSWER

Given, h(x)=x

3

+x

2

+x+1

h

′

(x)=3x

2

+2x+1

Here h

′

(x)>0 for all real x which means, h(x) is a continuous increasing function and will have no maxima or minima.

Answer 2

Step-by-step explanation:

given h(x) = x³+x²+x+1

calculating its derivative,

h'(x) = 3x² + 2x +1 = 2x² + (x+1)². sum of two squares is always positive, unless both are zero. Here x and x+1 cannot be zero at same time.

Therefore h'(x) is always positive. hene h(x) is ever increasing with no maxima or minima.